There isn't a universal answer to how Roth IRAs compound interest because a Roth IRA isn't a specific type of investment. Instead, Roth IRAs are a special type of retirement savings account that allows money to grow tax-free and be taken out tax-free at retirement. You can invest the money held in your Roth IRA in a range of options. The ones you use will determine how the money grows.
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Roth IRA Investment Options
Roth IRAs are typically invested in stocks and mutual funds, which grow or decline in value based on how well the investments perform. A good earnings report could bump up the value of your Roth IRA, while a poor report could cause a decline in value. On the other hand, you can hold money in your Roth IRA in deposit accounts, like certificates of deposit or even a savings account, in which case the interest compounds just like it would if the deposit account were not in your Roth IRA.